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The architectural identification of the ANN model is the primary important aspect of the modeling since inappropriate architecture may lead to under-fitting, over-fitting and computational overload. In the current research, the optimal number of neurons in the hidden layer was identified using a trial and error procedure by varying the number of hidden neurons from 2 to 20. Furthermore, the optimal network architecture was selected based on the one with minimum MSE. The final ANN architecture and the performance statistics of each model are shown in Table 4. It was observed that the ANN models produced slight variability in performance with the RMSE values varying from 0.473 to 0.176 mm/day, MAE values varying from 0.341 to 0.136 mm/day, and r values varying from 0.930 to 0.992 in the testing periods. ANN8, ANN7, ANN6, and ANN3 had similar performance that showed small differences between the RMSE, MAE, and r values. They were found to be better than the ANN1, ANN2, ANN4, and ANN5 models in the modeling of PMF-56 ET0. Similar to GA-SVM and SVM models, the ANN8 model with inputs of Tmin, Tmax, U2, RH, and Rs had the best performance (RMSE = 0.176 mm/day, MAE = 0.136 mm/day, and r = 0.992) among the ANN models.

Table 4

The structure and the performance statistics of the ANN models during the training and testing periods

Training periods
Testing periods
ModelInputStructurerRMSE mm/dayMAE mm/dayrRMSE mm/dayMAE mm/day
ANN1 2-12-1 0.939 0.439 0.315 0.941 0.473 0.341 
ANN2 3-4-1 0.959 0.352 0.259 0.967 0.361 0.280 
ANN3 3-11-1 0.971 0.301 0.174 0.986 0.245 0.174 
ANN4 3-13-1 0.952 0.380 0.289 0.930 0.482 0.349 
ANN5 4-6-1 0.964 0.330 0.243 0.968 0.347 0.266 
ANN6 4-4-1 0.974 0.280 0.176 0.990 0.224 0.169 
ANN7 4-6-1 0.982 0.232 0.156 0.985 0.232 0.155 
ANN8 5-11-1 0.984 0.223 0.141 0.992 0.176 0.136 
Training periods
Testing periods
ModelInputStructurerRMSE mm/dayMAE mm/dayrRMSE mm/dayMAE mm/day
ANN1 2-12-1 0.939 0.439 0.315 0.941 0.473 0.341 
ANN2 3-4-1 0.959 0.352 0.259 0.967 0.361 0.280 
ANN3 3-11-1 0.971 0.301 0.174 0.986 0.245 0.174 
ANN4 3-13-1 0.952 0.380 0.289 0.930 0.482 0.349 
ANN5 4-6-1 0.964 0.330 0.243 0.968 0.347 0.266 
ANN6 4-4-1 0.974 0.280 0.176 0.990 0.224 0.169 
ANN7 4-6-1 0.982 0.232 0.156 0.985 0.232 0.155 
ANN8 5-11-1 0.984 0.223 0.141 0.992 0.176 0.136 

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